The impact of the inherent optical properties (IOP) variability on the chlorophyll, Chl, retrieval from ocean color remote sensing algorithms is analyzed from an in situ data set covering a large dynamic range. The effect of the variability of the specific phytoplankton absorption coefficient, a phy/Chl, specific particulate backscattering coefficient, b bp/Chl, and colored detrital matter absorption to non-water absorption ratio, a cdm/anw, on the performance of standard operational algorithms is examined. This study confirms that empirical algorithms are highly dependent on the specifics IOP values (especially b bp/Chl and a cdm/anw): Chl is over-estimated in waters with specific IOP values higher than averaged values, and vice versa. These results clearly indicate the necessity to account for the influence of the specific IOP variability in Chl retrieval algorithms.
© 2010 OSA
Retrieval of chlorophyll-a concentration, Chl, from ocean color remote sensing is traditionally performed using blue-to-green reflectance ratio, BGR . This is mainly due to the fact that Chl (in mg.m−3), a common pigment to all phytoplankton species, absorbs strongly in the blue and weakly in the green spectral domain. Empirical ocean color algorithms were then developed from in situ and simultaneous measurements of Chl and remote sensing reflectance, R rs(λ) (in sr−1). R rs(λ) represents the ratio of the upwelling radiance to the downwelling irradiance above the sea surface at a given visible wavelength λ (in nm). These empirical algorithms are easy to develop but are by definition highly dependent on the data set used for their development. While BGR exhibits a net decrease from oligotrophic (blue) to eutrophic (green) waters, a large statistical dispersion is however noticeable around this mean trend (Fig. 1 ). This pattern may considerably affect the accuracy of the Chl retrieval from space, which can be much beyond the nominal uncertainty of 35% .
While the noise in the correlation between BGR and Chl is partly related to uncertainties in Chl and R rs(λ) in situ measurements, natural variability of inherent optical properties (IOP) undeniably affects this relationship. Among IOP, which depend on the concentration and nature of the various optically-significant components in presence, the absorption (a) and backscattering (b b) coefficients (both in m−1) are related to R rs: R rs(λ) ~b b(λ)/a(λ). While the first order variability of IOP is mainly driven by Chl in oceanic waters, the second order variability observed around the IOP vs. Chl relationships is directly related to the specific IOP variability. For a given chlorophyll concentration, variations in the absorption and backscattering spectra affect the spectral values of R rs(λ) and hence the BGR. For example, variations in algal community size structure modify, through the package effect, the phytoplankton absorption spectrum therefore affecting the remote sensing of phytoplankton pigments [3,4]. During coccolithophore blooms, coccolithes detached from the phytoplankton cells greatly contribute to increase b b , therefore inducing an overestimation of the Chl derived from ocean color remote sensing . Variation in the phytoplankton assemblages can also have a relevant impact, as large as 50%, on the Chl retrieval as pointed out by Alvain et al.  from ocean color remote sensing data. The respective proportion of phytoplankton, non-algal particles and colored dissolved organic matter also influences the amplitude and spectral behaviour of R rs. For instance, Stramska et al.  have shown from in situ measurement performed in the north polar Atlantic that variations in the concentrations of detrital particles and accessory pigments may drastically affect the Chl retrieval. In the same way, absorption by colored dissolved organic matter and detrital particles may lead to large errors in the estimation of Chl loads [9–11]. Similar conclusions were recently reached by Brown et al.  who showed that the second order variability in the satellite ocean color signal for a given chlorophyll concentration is mainly explained by the amount of colored dissolved organic matter and particulate backscattering.
Previous studies have provided evidences that the estimation of Chl from ocean color remote sensing may be affected by IOP variability. These studies are generally based on local in situ data sets or satellite remote sensing data which include many sources of errors. Indeed, uncertainties on the Chl retrieval from ocean color remote sensing have different origins: atmospheric correction errors, bio-optical algorithm uncertainties, mismatches in spatial scales, as well as in situ measurement errors. The aim of the present paper is to examine the origin of the scatter in the BGR vs. Chl relationship from an in situ data set covering a large dynamic range. The impact of the variability of different specific IOP on the Chl retrieval is addressed in order to identify and compare their respective influence.
2. Data and method
In this study we use the NOMAD data set  together with data collected during other oceanographic cruises occurring in the French Guyana coastal waters  and in the English Channel and North sea  which have been recently included in the NOMAD data set. Using this data set, covering oceanic and coastal waters, we analyse the impact of three specific IOP on the dispersion in the BGR vs. Chl relationship. The first one is the specific phytoplankton absorption coefficient at 443 nm (a phy/Chl). A large natural variability in the a phy vs. Chl relationship has long been pointed out. a phy/Chl may indeed vary by a factor of about 4 for a given Chl concentration . This biological noise is mostly driven by the average size of algal populations (i.e. package effect) rather than by the proportion of accessory pigments relative to Chl . The second parameter is the specific particulate backscattering coefficient at 532 nm (b bp/Chl). Field measurements performed in various oceanic areas have shown that b bp exhibits a high variability (about a factor of 4) for a given chlorophyll concentration [17,18]. While the b bp/Chl variability is driven by particle size distribution, refractive index and shape of the bulk particulate matter, the respective influence of each of these factors is still poorly known. The last specific IOP is the ratio of the colored detrital matter absorption coefficient, a cdm, to the non-water absorption coefficient, a nw, at 443 nm (a nw = a phy + a cdm). The relative contribution of colored detrital matter absorption to non water absorption, which may drastically modify the spectral shape of R rs, is highly variable in natural waters being dependent on various biogeochemical and physical processes.
The whole data set used in this study encompasses 862 pairs of (Chl, R rs) data points for which one specific IOPs is at least available (760 are from NOMAD). Phytoplankton and colored detrital matter absorption measurements are available for 762 (Chl, BGR) data points, whereas particulate backscattering measurements are available for 323 (Chl, BGR) data points. This difference does not significantly affect the conclusions of this study since the b bp/Chl, a phy/Chl, and a cdm/a nw data points are distributed over roughly similar chlorophyll ranges. The proportion of data with relatively low chlorophyll concentration (Chl ≤ 0.5 mg.m−3) is however lower in the bbp/Chl data set (19%) than in the aphy/Chl and a cdm/a nw data sets (36% for both). The median values of b bp/Chl, a phy/Chl, and a cdm/a nw are 0.0024 m2mg−1, 0.054 m2mg−1, and 0.61 respectively. The coefficient of variation (i.e. a ratio of standard deviation to the mean) for b bp/Chl, a phy/Chl, and a cdm/a nw are 152%, 53%, and 23%, respectively. a phy(443) increases with Chl according to a power law in good agreement with standard parameterisations . A least square fit performed on the present data set provides the following relationship: a phy(443) = 0.0543Chl −0.764(N = 762, r2 = 0.91), which is very similar to the one developed by Bricaud et al.  on an large oceanic data set [Fig. 2(a) ]. In the same way, the b bp(532)-Chl dependency exhibits a non linear character, as expressed by the exponent 0.704:
This relationship is slightly modified by removing data collected in very turbid waters:
The threshold value for discriminating very turbid waters is fixed from Eq. (1) and Fig. 2(a), in a similar way as performed for the scattering coefficient [19,20]. In practice, stations with b bp/Chl values greater than 0.009 mg−1m2 are classified as very turbid water. The non-turbid water relationship describe by Eq. (2) is very close to the one found by Huot et al.  from measurements performed in the upper layer of the eastern south Pacific ocean [Fig. 2(b)]. Similarly to a phy(443) and b bp(532) a relatively good relationship is also found between a cdm(443) and Chl [Fig. 2(c)]:
This result is coherent with the study of Siegel et al.  performed on remote sensing ocean color data who found a significant determination coefficient (r = 0.58) between a cdm(443) and Chl (their Fig. 3 and Table 3). Note that the exponent 0.63 is similar to the one found by Morel  between the absorption by colored dissolved organic matter, a cdom, and Chl, which is expected as a cdm is dominated by a cdom for nearly all the ocean . The different observations reported here point out that the present data set, which covers a wide range of bio-optical conditions, is consistent with averaged relationships developed between IOP and Chl during the last decade.
The impact of the variability of these three specific IOP on the Chl retrieval is tested through the Chl vs BGR relationships described by the operational algorithms used for SeaWiFS (OC4.v4) and MODIS (OC3M) . Each specific IOP sub data set is split into four equal parts computed according to Hyndman and Fan recommendation . The first quartile cuts off the lowest 25% of the data. The corresponding sub data set is named DS1. The second quartile, which is equal to the median, cuts data set in half (DS2 and DS3), and third quartile cuts off highest 25% of data (DS4). The impact of the specific IOP on the Chl retrieval is evaluated through correlation analysis, root mean square log error, RMS, and average difference, AD. RMS is calculated as follows: RMS = (∑[log(Chl retrieved)-log(Chl in situ)]2/N)0.5, and AD is defined as: AD = (∑[log(Chl retrieved)-log(Chl in situ)]/N (where N is the number of samples).
3. Results and discussion
The overall comparison between in situ Chl and OC4v4 or OC3M retrieved Chl (N = 862) indicates a relatively good agreement for the whole data set [Fig. 3(a) ]. The RMS, AD, and r2 values are 25.25%, 3.80%, and 0.88 using OC4v4 (N = 862), and 24.80%, −5.04%, and 0.88 using OC3M (N = 862). These results are consistent with the conclusions of Moore et al.  which were based on a much larger in situ data set. The scatter of the data points around the 1:1 line indicates that Chl may be over- or under-estimated by a factor of 2 within the whole chlorophyll range.
The comparison is now performed for the three specific IOP data sets to analyse the impact of the natural variability of IOP on the Chl retrieval accuracy [Figs. 3 (b), 3(c), 3(d)]. The RMS, AD, and r2 values calculated for the data sets associated with each specific IOP are equivalent to those calculated for the whole data set (Table 1 ). For the three specific IOP data sets the relative error on the Chl retrieval may reach 100% over the whole Chl range (i.e. the data points on the 1:2 and 2:1 lines). While DS2 and DS3 are generally close to the 1:1 line of the in situ Chl vs satellite Chl relationships, this is not the case for DS1 and DS4. The points belonging to DS1 and DS4 are those for which the corresponding specific IOP values are respectively the lowest and greatest. The median and variation coefficient (in %) values of b bp/Chl, a phy/Chl, and a cdm/a nw are 0.0009 m2mg−1(37%), 0.0294 m2mg−1 (25%), and 0.443 (18%) for DS1. The median values respectively jump to 0.0066 m2mg−1 (94%), 0.098 m2mg−1 (27%), and 0.757 (8%) for DS4. Therefore, the median b bp/Chl, aphy/Chl, and a cdm/a nw values vary respectively by a factor of 7.3, 3.3, and 1.7 between DS1 and DS4. When the very turbid data points are discarded from the b bp/Chl data set, the median value of b bp/Chl increases from 0.0008 m2mg−1 (34%) to 0.0045 (24%) m2mg−1 between DS1 and DS4 (a factor of 5.6). The average difference, which estimates the overall bias, clearly indicates that both OC4v4 and OC3M underestimate Chl (negative AD values) in DS1 and overestimate Chl (positive AD values) in DS4, whatever the specific IOP data set (Table 1). For instance, Chl is underestimated by 17.18% in DS1 and overestimated by 20.75% in DS4 for the b bp/Chl data set and using OC4v4. Note that the AD values for the b bp/Chl data set are similar for the non-very turbid data set (−17.2% for DS1 and 18.4% for DS4). Histograms showing the frequency distribution of the relative difference between the measured and estimated Chl also emphasize a significant shift from negative (under-estimation) to positive (over-estimation) values when the data set moves from DS1 to DS4 (Fig. 4 ). For instance, the median value of the relative difference between in situ and inversed OC4v4 Chl increases from −33% to 60% when b bp/Chl increases between DS1 and DS4, respectively (same trend for OC3M). In contrast, this increase is lower for the two other specific IOP, as the median value of the relative Chl difference increases from −22% (−18.7) to 9.6% (27.4) when a phy/Chl (a cdm/a nw) increases between DS1 and DS4. These results clearly indicate that Chl is underestimated by empirical algorithms in waters with specific IOP values “lower” than averaged values, and vice versa. Averaged values are calculated from the empirical relationships developed from in situ measurements of IOP and Chl.
Moreover, the latter features confirm that waters with higher b bp/Chl, aphy/Chl, or a cdm/a nw ratios will be seen greener by standard empirical algorithms. This is consistent with previous works performed on in situ or satellite measurements [11,26,27]. Due to differences in the spectral domains influenced by b bp, a phy, and a cdm the three specific IOPs considered affect BGR in different ways. While a phy and a cdm mainly affect the blue spectral domain, b bp influences the green region. Based on the present data set, one may additionally stress that the impact of b bp/Chl on the BGR vs. Chl variability is much higher than that of a phy/Chl and a cdm/a nw. This difference is mainly explained by the greater range of variability for b bp/Chl when compared to that for a phy/Chl and a cdm/a nw. Note however that for the same range of variability absorption by colored dissolved organic matter is expected to have a greater impact on the BGR vs. Chl relationship than the particulate backscattering coefficient . The b bp/Chl variability as well as the relative proportion between molecular and particular scattering directly affects the blue-to-green backscattering ratio, and consequently the BGR. Importantly, while the median value of a phy/Chl varies twice as much as that of a cdm/a nw between DS1 and DS4, the respective impact of these two specifics IOP on the Chl retrieval is similar. This pattern may be explained by decomposing the green-to-blue absorption ratio (proportional to BGR) as: (a w(550) + a phy(550) + a cdm(550))/a(440). The evolution of a w(550)/a(440), a cdm(550)/a(440), and a phy(550)/a(440) is examined in function of changes in the Chl load using the present in situ data set [Fig. 5(a) ] as well as a synthetic data set [Fig. 5(b)] generated in the frame of a working group on ocean-colour algorithm . Based on these two different data sets a cdm(550)/a(440) is roughly constant over the whole chlorophyll range (a cdm(550)/a(440)~0.13 ± 0.05 for the in situ data set), whereas a phy(550)/a(440) slightly increases with Chl according to: Log(a phy(550)/a(440)) = 0.27Log(Chl)-1.30 (r2 = 0.38) for the in situ data set. a cdm(550)/a(440) is therefore generally much higher than a phy(550)/a(440). For instance, a cdm(550)/a(440) is greater than a phy(550)/a(440) by a factor of 3.6 and 1.9 for Chl of 0.3 and 3.0 mg.m−3, respectively. Hence, a given variation in a cdm(550)/a(440) has a greater effect on BGR than a variation of similar amplitude in a phy(550)/a(440).
Improvement of bio-optical algorithms dedicated to the Chl retrieval from ocean color remote sensing should account for specific IOP variability. Simultaneous retrieval of IOP and Chl, as already performed from semi-analytical algorithms (e.g. ), allows to partly take into account such variability (even though some specific IOP values have to be fixed in these algorithms). Classification of R rs spectra, prior to application of specific bio-optical algorithms, may also represent a valuable way to improve the Chl retrieval (e.g. [2,15]).
This work was supported by Centre National d’Etude Spatiale in the frame of the COULCOT project (TOSCA program). The authors would also like to thank the many scientists who have shared their in situ data in the NOMAD public database, which has made this work possible.
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